Subject: [mg125410] How to define a specific definite integral result in Mathematica

From: Antonio Alvaro Ranha Neves <aneves at gmail.com>

Date: Tue, 13 Mar 2012 03:02:00 -0500 (EST)

Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Dear Mathematica users,
I'd like to use the following integral for symbolic computation,
Integrate[
Sin[a] Exp[I r Cos[b] Cos[a]] LegendreP[n, m, Cos[a]] BesselJ[m,
r Sin[b] Sin[a]], {a, 0, \[Pi]}]
whose result is
2 I^(n - m) LegendreP[n, m, Cos[b]] SphericalBesselJ[n, r]
is there a way to make Mathematica "learn" this result, so that I can work with symbolic computation of the integrand?
Thanks,
Antonio